#
PH5023 Monte Carlo Radiation Transport Techniques

## Kenny Wood (kw25)

## Overview

This module introduces the theory and practice behind Monte Carlo radiation
transport codes for use in physics, astrophysics, atmospheric physics, neutron
transport for criticality calculations, and
medical physics. Core topics that will be covered include:
recap of basic radiation transfer;
techniques for sampling from probability distribution functions; an
isotropic scattering code; computing the radiation field, pressure,
temperature, and ionisation structure; programming skills required to write
Monte Carlo codes; code speed-up techniques and parallel computing;
three-dimensional codes.
The module will comprise lectures and at least two taught lab sessions. The
lecture notes will be provided on-line below both in PDF format and
read-only pptx files with audio. The lab sessions will
introduce the basic Fortran programming skills required for the module. By
the end of the lab
sessions each student will have written their own Monte Carlo
codes to sample from probability distribution functions and also a code that
simulates isotropic scattering of radiation from a point source at the
centre of a unifom density sphere. Another lab session will follow on from
lectures that describe a publicly available three dimensional scattering code.
During this lab session,
students will be led through the 3D code's subroutines and how to adapt them
for their own three dimensional radiation transport simulations.

**Prerequsites:** PH2012: Physics 2B, plus at least 1 of the following:
AS3013: Computational Astrophysics, PH3080: Computational Physics,
PH3081: Mathematics for Physicists, PH3082: Mathematics for Chemistry/Physics

## Texbooks

A Monte Carlo Primer by Dupree & Fraley. This book focuses on neutron
transport but the techniques are the same for photon transport and it
has lots of programming examples. Several copies of this have been
bought for the Physics & Astronomy library.
Steve Jacques (who gave three guest lectures in 2014)
has supplied this review chapter on Monte Carlo simulations
of photon transport in biological tissue:
PDF

## Lectures

PDFs of the lecture slides are available with two slides per page. The Power Point
files containing audio on each slide are available as read-only pptx files.

## Monte Carlo Radiation Transport on a 3D Cartesian Grid

I have set up a 3D grid code to compute the average number of scatterings
of photons emitted from the centre of a uniform density sphere. The
emission and scattering are both assumed to be isotropic. The code algorithms
and subroutines are described in the lecture "MCRT on a 3D Cartesian Grid."
You can download a tar file of the code
here. To unpack the tarball, type "tar - xvf grid.tar"
and this will give you eight fortran files, two txt files, an input.params
file, a README, and a Makefile. To get started
type "make" and this will produce an executable file called "mcgrid." When
you run this the code will generate some output to the screen. The code is
set up for a simulation where the optical depth across the sphere's diameter
is 20 (radial optical depth of 10). The average number of scatterings for
this optical depth and input parameters given is 57.35.
The code writes out a file "density.dat" which is an unformatted fortran
file comprising the 3D density grid. You may use this short fortran code,
read_write.f to read in the density grid and
write out a 2D slice through the grid. You can then import the output 2D
slice into a plotting program (gnuplot, IDL, Mathematica, etc) to display
the slice as a 2D image.

## Resources

Here are some links to texts and other Monte Carlo lectures and courses that
I've found on random walks around the internet...
**Texts, Notes, and Review Chapters:**

The classic text by Cashwell and Everett (1957): A Practical Manual on the
Monte Carlo Method for Random Walk Problems
PDF

Monte Carlo Techniques of Electron and Photon Transport for Radiation
Dosimetry by Rogers and Bielajew PDF

**Historical development of Monte Carlo Radiation Transfer**

The following files are from the Los Alamos archive and give a very
enjoyable overview of the development of MCRT.

Letter from John von Neumann to Bob
Richtmyer, 1947

The Beginning of the Monte Carlo Method
by Nick Metropolis

Stan Ulam, John von Neumann, and the Monte
Carlo Method, by Roger Eckhardt

Metroplois, Monte Carlo, and the MANIAC, by
H.L. Anderson

**Lecture Courses and Summer Schools**

St Andrews Monte Carlo Summer School